Mechanisms and Models of Seismic Attenuation

Seismic attenuation is a subject of great interest for both industry and academia. In exploration seismology, wave attenuation must be well understood for interpreting seismic data and laboratory experiments with rocks, and improving the quality and resolution of reflection imaging of the subsurface. To achieve such understanding, mechanisms of seismic attenuation and the associated physical models need to be studied in detail. This dissertation focuses on analyzing several attenuation mechanisms and building first-principle mathematical models for them. The effects of seismic attenuation can be broadly subdivided into two groups: 1) caused by inelasticity of the material and 2) caused by small-scale elastic structures of the material or subsurface. From the first of these groups, I study solid viscosity and internal friction due to squirt flows and wave-induced fluid flows (WIFF) at different scales. This approach is based on a new rheological law called the General Linear Solid (GLS) and recently developed to describe macroscopic inelastic effects in multiphase solids. The GLS is a model composed by time/frequency independent parameters and based on Lagrangian continuum mechanics. By utilizing the GLS framework, I extend the well known-model called the Standard Linear Solid (SLS) to include internal inertial forces, which explains the primary wave and reveals additional highly diffusive wave modes. I also use the GLS to model P-waves with squirt flow dissipation by different configurations of the density, moduli, drag and solid viscosity matrices. Seismic wave attenuation may not only be caused by inelastic properties but also by elastic processes such as reflectivity and scattering. I examine two types of such effects of the elastic structure of the material. First, in a laboratory experiment with several rock types, there is a modest influence of sample size on the measured level of attenuation and modulus dispersion. Second, in a field experiment aimed at measuring Q from seismic reflectivity, the effect of elastic layering can be extremely strong and even completely equivalent to that of the Q. An important general observation from this study is that amplitude decays and phase delays measured from reflection seismic data can always be interpreted as either caused by inelasticity or by small-scale elastic structures. An important complementary goal of studying the mechanisms and effects of seismic attenuation consists in correcting for its effects in seismic records and increasing the resolution of seismic images. In this dissertation, I briefly consider attenuation-correction techniques and develop a novel method for such correction by using time-domain deconvolution. Synthetic and field data are used to illustrate and test the performance of this approach

Accurate and automatic refraction statics in large 3D seismic dataset

Inversion for refraction statics is a key part of three-dimensional (3D) reflection seismic processing. The present thesis has two primary goals directed toward improvement of refraction statics inversion. First, I attempt to improve the quality of the travel-time data right at the beginning of the processing sequence and before any inversion. Any error in the travel times or geometry caused during acquisition or processing would propagate into the resulting model and may harm the resulting image. To implement rigorous, model-independent data quality control, I view the first-arrival travel times as surfaces in 3D, which allows utilization of the travel-time reciprocity condition to check for errors in geometry and in first-arrival picking. The second goal of this study is in development of a new inversion approach for refraction statics specifically for 3D seismic datasets. The first-break travel-times are decomposed by using a ô-p parameterization, which allows an automatic derivation of a high-quality initial subsurface model. This model is further improved by using accurate, multi-layer ray-tracing and inversion techniques to obtain accurate refraction statics. An iterative inversion scheme based on the Simultaneous Iterative Reconstruction Technique is utilized, and its performance is measured and discussed. To assess the quality of the inverse and establish the optimal grid sizes, I use several types of resolution tests. Finally, the surface consistent statics is calculated and applied to a real dataset from southern Saskatchewan. A comparison of the resulting statics model with statics calculated by using standard industry software is made, and the statics correction is incorporated in seismic processing. An overall result of this study is in demonstration that the fully 3D, ô-p based travel-time inversion method works, is applicable to large seismic datasets, and results in detailed shallow subsurface models and reliable statics solutions. Several recommendations for extending and improving the proposed approaches are also made

Full waveform inversion procedures with irregular topography

Full waveform inversion (FWI) is a form of seismic inversion that uses data residual, found as the misfit, between the whole waveform of field acquired and synthesized seismic data, to iteratively update a model estimate until such misfit is sufficiently reduced, indicating synthetic data is generated from a relatively accurate model. The aim of the thesis is to review FWI and provide a simplified explanation of the techniques involved to those who are not familiar with FWI. In FWI the local minima problem causes the misfit to decrease to its nearest minimum and not the global minimum, meaning the model cannot be accurately updated. Numerous objective functions were proposed to tackle different sources of local minima. The ‘joint deconvoluted envelope and phase residual’ misfit function proposed in this thesis aims to combine features of these objective functions for a comprehensive inversion. The adjoint state method is used to generate an updated gradient for the search direction and is followed by a step-length estimation to produce a scalar value that could be applied to the search direction to reduce the misfit more efficiently. Synthetic data are derived from forward modelling involving simulating and recording propagating waves influenced by the mediums’ properties. The ‘generalised viscoelastic wave equation in porous media’ was proposed by the author in sub-chapter 3.2.5 to consider these properties. Boundary layers and conditions are employed to mitigate artificial reflections arising from computational simulations. Linear algebra solvers are an efficient tool that produces wavefield vectors for frequency domain synthetic data. Regions with topography require a grid generation scheme to adjust a mesh of nodes to fit into its non-quadrilateral shaped body. Computational co-ordinate terms are implemented within wave equations throughout topographic models where a single point in the model in physical domain are represented by cartesian nodes in the computational domains. This helps to generate an accurate and appropriate synthetic data, without complex modelling computations. Advanced FWI takes a different approach to conventional FWI, where they relax upon the use of misfit function, however none of their proponents claims the former can supplant the latter but suggest that they can be implemented together to recover the true model.Open Acces

Estimation of Radio Channel Parameters

Kurzfassung Diese Dissertation behandelt die Schätzung der Modellparameter einer Momentanaufnahme des Mobilfunkkanals. Das besondere Augenmerk liegt zum einen auf der Entwicklung eines generischen Datenmodells für den gemessenen Funkkanal, welches für die hochauflösende Parameterschätzung geeignet ist. Der zweite Schwerpunkt dieser Arbeit ist die Entwicklung eines robusten Parameterschätzers für die Bestimmung der Parameter des entworfenen Modells aus Funkkanalmessdaten. Entsprechend dieser logischen Abfolge ist auch der Aufbau dieser Arbeit. Im ersten Teil wird ausgehend von einem aus der Literatur bekannten strahlenoptischen Modell eine algebraisch handhabbare Darstellung von beobachteten Wellenausbreitungspfaden entwickelt. Das mathematische Modell erlaubt die Beschreibung von SISO (single-input-single-output)- Übertragungssystemen, also von Systemen mit einer Sendeantenne und einer Empfangsantenne, als auch die Beschreibung von solchen Systemen mit mehreren Sende- und/oder Empfangsantennen. Diese Systeme werden im Allgemeinen auch als SIMO- (single-input-multiple-output), MISO- (multiple-input-single-output) oder MIMO-Systeme (multiple-input-multiple-output) bezeichnet. Im Gegensatz zu bekannten Konzepten enthält das entwickelte Modell keine Restriktionen bezüglich der modellierbaren Antennenarrayarchitekturen. Dies ist besonders wichtig in Hinblick auf die möglichst vollständige Erfassung der räumlichen Struktur des Funkkanals. Die Flexibilität des Modells ist eine Grundvoraussetzung für die optimale Anpassung der Antennenstruktur an die Messaufgabe. Eine solche angepasste Antennenarraystruktur ist zum Beispiel eine zylindrische Anordnung von Antennenelementen. Sie ist gut geeignet für die Erfassung der räumlichen Struktur des Funkkanals (Azimut und Elevation) in so genannten Outdoor- Funkszenarien. Weiterhin wird im ersten Teil eine neue Komponente des Funkkanaldatenmodells eingeführt, welche den Beitrag verteilter (diffuser) Streuungen zur Funkübertragung beschreibt. Die neue Modellkomponente spielt eine Schlüsselrolle bei der Entwicklung eines robusten Parameterschätzers im Hauptteil dieser Arbeit. Die fehlende Modellierung der verteilten Streuungen ist eine der Hauptursachen für die begrenzte Anwendbarkeit und die oft kritisierte fehlende Robustheit von hochauflösenden Funkkanalparameterschätzern, die in der Literatur etabliert sind. Das neue Datenmodell beschreibt die so genannten dominanten Ausbreitungspfade durch eine deterministische Abbildung der Pfadparameter auf den gemessenen Funkkanal. Der Beitrag der verteilten Streuungen wird mit Hilfe eines zirkularen mittelwertfreien Gaußschen Prozesses beschrieben. Die Modellparameter der verteilten Streuungen beschreiben dabei die Kovarianzmatrix dieses Prozesses. Basierend auf dem entwickelten Datenmodell wird im Anschluss kurz über aktuelle Konzepte für Funkkanalmessgeräte, so genannte Channel-Sounder, diskutiert. Im zweiten Teil dieser Arbeit werden in erster Linie Ausdrücke zur Bestimmung der erzielbaren Messgenauigkeit eines Channel-Sounders abgeleitet. Zu diesem Zweck wird die untere Schranke für die Varianz der geschätzten Modellparameter, das heißt der Messwerte, bestimmt. Als Grundlage für die Varianzabschätzung wird das aus der Parameterschätztheorie bekannte Konzept der Cramér-Rao-Schranke angewandt. Im Rahmen der Ableitung der Cramér-Rao-Schranke werden außerdem wichtige Gesichtspunkte für die Entwicklung eines effizienten Parameterschätzers diskutiert. Im dritten Teil der Arbeit wird ein Schätzer für die Bestimmung der Ausbreitungspfadparameter nach dem Maximum-Likelihood-Prinzip entworfen. Nach einer kurzen Übersicht über existierende Konzepte zur hochauflösenden Funkkanalparameterschätzung wird die vorliegende Schätzaufgabe analysiert und in Hinsicht ihres Typs klassifiziert. Unter der Voraussetzung, dass die Parameter der verteilten Streuungen bekannt sind, lässt sich zeigen, daß sich die Schätzung der Parameter der Ausbreitungspfade als ein nichtlineares gewichtetes kleinstes Fehlerquadratproblem auffassen lässt. Basierend auf dieser Erkenntnis wird ein generischer Algorithmus zur Bestimmung einer globalen Startlösung für die Parameter eines Ausbreitungspfades vorgeschlagen. Hierbei wird von dem Konzept der Structure-Least-Squares (SLS)-Probleme Gebrauch gemacht, um die Komplexität des Schätzproblems zu reduzieren. Im folgenden Teil dieses Abschnitts wird basierend auf aus der Literatur bekannten robusten numerischen Algorithmen ein Schätzer zur genauen Bestimmung der Ausbreitungspfadparameter abgeleitet. Im letzten Teil dieses Abschnitts wird die Anwendung unterraumbasierter Schätzer zur Bestimmung der Ausbreitungspfadparameter diskutiert. Es wird ein speichereffizienter Algorithmus zur Signalraumschätzung entwickelt. Dieser Algorithmus ist eine Grundvoraussetzung für die Anwendung von mehrdimensionalen Parameterschätzern wie zum Beispiel des R-D unitary ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) zur Bestimmung von Funkkanalparametern aus MIMO-Funkkanalmessungen. Traditionelle Verfahren zur Signalraumschätzung sind hier im Allgemeinen nicht anwendbar, da sie einen zu großen Speicheraufwand erfordern. Außerdem wird in diesem Teil gezeigt, dass ESPRIT-Algorithmen auch zur Parameterschätzung von Daten mit so genannter versteckter Rotations-Invarianzstruktur eingesetzt werden können. Als Beispiel wird ein ESPRIT-basierter Algorithmus zur Richtungsschätzung in Verbindung mit multibeam-Antennenarrays (CUBA) abgeleitet. Im letzten Teil dieser Arbeit wird ein Maximum-Likelihood-Schätzer für die neue Komponente des Funkkanals, welche die verteilten Streuungen beschreibt, entworfen. Ausgehend vom Konzept des iterativen Maximum-Likelihood-Schätzers wird ein Algorithmus entwickelt, der hinreichend geringe numerische Komplexität besitzt, so dass er praktisch anwendbar ist. In erster Linie wird dabei von der Toeplitzstruktur der zu schätzenden Kovarianzmatrix Gebrauch gemacht. Aufbauend auf dem Schätzer für die Parameter der Ausbreitungspfade und dem Schätzer für die Parameter der verteilten Streuungen wird ein Maximum-Likelihood-Schätzer entwickelt (RIMAX), der alle Parameter des in Teil I entwickelten Modells der Funkanalmessung im Verbund schätzt. Neben den geschätzten Parametern des Datenmodells liefert der Schätzer zusätzlich Zuverlässigkeitsinformationen. Diese werden unter anderem zur Bestimmung der Modellordnung, das heißt zur Bestimmung der Anzahl der dominanten Ausbreitungspfade, herangezogen. Außerdem stellen die Zuverlässigkeitsinformationen aber auch ein wichtiges Schätzergebnis dar. Die Zuverlässigkeitsinformationen machen die weitere Verarbeitung und Wertung der Messergebnisse möglich.The theme of this thesis is the estimation of model parameters of a radio channel snapshot. The main focus was the development of a general data model for the measured radio channel, suitable for both high resolution channel parameter estimation on the one hand, and the development of a robust parameter estimator for the parameters of the designed parametric radio channel model, in line with this logical work flow is this thesis. In the first part of this work an algebraic representation of observed propagation paths is developed using a ray-optical model known from literature. The algebraic framework is suitable for the description of SISO (single-input-single-output) radio transmission systems. A SISO system uses one antenna as the transmitter (Tx) and one antenna as the receiver (Rx). The derived expression for the propagation paths is also suitable to describe SIMO (single-input-multiple-output), MISO (multiple-input-single-output), and MIMO (multiple-input-multiple-output) radio channel measurements. In contrast to other models used for high resolution channel parameter estimation the derived model makes no restriction regarding the structure of the antenna array used throughout the measurement. This is important since the ultimate goal in radio channel sounding is the complete description of the spatial (angular) structure of the radio channel at Tx and Rx. The flexibility of the data model is a prerequisite for the optimisation of the antenna array structure with respect to the measurement task. Such an optimised antenna structure is a stacked uniform circular beam array, i.e., a cylindrical arrangement of antenna elements. This antenna array configuration is well suited for the measurement of the spatial structure of the radio channel at Tx and/or Rx in outdoor-scenarios. Furthermore, a new component of the radio channel model is introduced in the first part of this work. It describes the contribution of distributed (diffuse) scattering to the radio transmission. The new component is key for the development of a robust radio channel parameter estimator, which is derived in the main part of this work. The ignorance of the contribution of distributed scattering to radio propagation is one of the main reasons why high-resolution radio channel parameter estimators fail in practice. Since the underlying data model is wrong the estimators produce erroneous results. The improved model describes the so called dominant propagation paths by a deterministic mapping of the propagation path parameters to the channel observation. The contribution of the distributed scattering is modelled as a zero-mean circular Gaussian process. The parameters of the distributed scattering process determine the structure of the covariance matrix of this process. Based on this data model current concepts for radio channel sounding devices are discussed. In the second part of this work expressions for the accuracy achievable by a radio channel sounder are derived. To this end the lower bound on the variance of the measurements i.e. the parameter estimates is derived. As a basis for this evaluation the concept of the Cramér-Rao lower bound is employed. On the way to the Cramér-Rao lower bound for all channel model parameters, important issues for the development of an appropriate parameter estimator are discussed. Among other things the coupling of model parameters is also discussed. In the third part of this thesis, an estimator, for the propagation path parameters is derived. For the estimator the 'maximum-likelihood' approach is employed. After a short overview of existing high-resolution channel parameter estimators the estimation problem is classified. It is shown, that the estimation of the parameters of the propagation paths can be understood as a nonlinear weighted least squares problem, provided the parameters of the distributed scattering process are known. Based on this observation a general algorithm for the estimation of raw parameters for the observed propagation paths is developed. The algorithm uses the concept of structured-least-squares (SLS) and compressed maximum likelihood to reduce the numerical complexity of the estimation problem. A robust estimator for the precise estimation of the propagation path parameters is derived. The estimator is based on concepts well known from nonlinear local optimisation theory. In the last part of this chapter the application of subspace based parameter estimation algorithms for path parameter estimation is discussed. A memory efficient estimator for the signal subspace needed by, e.g., R-D unitary ESPRIT is derived. This algorithm is a prerequisite for the application of signal subspace based algorithms to MIMO-channel sounding measurements. Standard algorithms for signal subspace estimation (economy size SVD, singular value decomposition) are not suitable since they require an amount of memory which is too large. Furthermore, it is shown that ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) based algorithms can also be employed for parameter estimation from data having hidden rotation invariance structure. As an example an ESPRIT algorithm for angle estimation using circular uniform beam arrays (circular multi-beam antennas) is derived. In the final part of this work a maximum likelihood estimator for the new component of the channel model is developed. Starting with the concept of iterative maximum likelihood estimation, an algorithm is developed having a low computational complexity. The low complexity of the algorithm is achieved by exploiting the Toeplitz-structure of the covariance matrix to estimate. Using the estimator for the (concentrated, dominant, specular-alike) propagation paths and the parametric estimator for the covariance matrix of the process describing the distributed diffuse scattering a joint estimator for all channel parameter is derived (RIMAX). The estimator is a 'maximum likelihood' estimator and uses the genuine SAGE concept to reduce the computational complexity. The estimator provides additional information about the reliability of the estimated channel parameters. This reliability information is used to determine an appropriate model for the observation. Furthermore, the reliability information i.e. the estimate of the covariance matrix of all parameter estimates is also an important parameter estimation result. This information is a prerequisite for further processing and evaluation of the measured channel parameters

Experimental seismic surveys of the Trans-Hudson Orogen

Two experimental seismic surveys were collected in the 1991 LITHOPROBE Trans-Hudson Orogen (THO) data acquisition program. The purpose of the coincident dynamite and vibroseis reflection surveys was to compare crustal images obtained using high-fold low-energy and low-fold high-energy sources. On single-fold field records, signal amplitudes from explosive sources are consistently 50 dB higher than on the corresponding vibroseis records. The vibroseis final stack exhibits better defined upper-crustal reflectivity due primarily to the higher fold. However, at lower-crustal and Moho levels, the dynamite data provides images which are equal or superior to those obtained from the vibroseis data. The dynamite source not only allowed deeper signal penetration but also succeeded in mapping of a number of subcrustal reflections not identified in previous vibroseis data. These new seismic images indicate that the crustal root is not simple depression on the upper-mantle as was inferred initially but a broad (3 s) zone of reflectivity that dips west and extends more than 10 km below the younger regional Moho. Moreover, the dynamite data also indicates that diffraction patterns, detected at lower crustal and Moho depths, have large apertures which permitted proper migration of these lower crustal events. Four vibroseis expanding spread profiles (ESP) were also acquired during the data acquisition program to obtain more detailed and accurate velocity structure. These profiles, with a maximum offset of 18 km, were centered on areas where prominent crustal reflectivity was detected by the regional vibroseis survey. The small source stepout distance (100 m) generated high-fold ($>$30) data. Extensive modeling was carried out to estimate the offset range within which each traveltime approximation and velocity analysis technique may be implemented. The results reveal that velocity estimation becomes more robust and accurate when crustal seismic surveys utilize longer offsets than commonly used. These larger source-receiver separations, however, must be generally limited to offset/depth ratios not exceeding 1.5 when conventional velocity analysis techniques, based on the hyperbolic moveout assumptions, are implemented. Besides the semblance method two velocity estimators adapted to crustal studies, namely the covariance and the $\tau$ - p techniques, were tried. The former yielded the highest resolution followed by the semblance and the $\tau$ - p methods. Resolution of the semblance estimator for a maximum offset of 36 km is equal to that of the covariance method with a corresponding offset of 18 km for mid-crustal reflectors. The advantages provided by the long-offset data acquisition include increased S/N ratio and a greater number of traces with sufficiently large moveouts whichimproved velocity resolution, especially below mid-crustal depths. To achieve similar advantages in a regional crustal reflection survey would require the adoption of longer spread lengths than those presently implemented in standard data acquisition procedures

Applications of 2D and 3D full waveform tomography in acoustic and viscoacoustic complex media

Full waveform tomography (FWT) is a high-resolution imaging method to exploit the full richness of recorded waveforms. It is able to resolve subsurface structures smaller than a wavelength. In this work I developed 2D and 3D time-domain implementations of acoustic FWT including its optimization with respect to methodological and technical aspects. I accomplished several synthetic feasibility studies with applications to seismic data computed in cross-well or reflection experiments

Seismic Full-Waveform Inversion of 3D Field Data – From the Near Surface to the Reservoir

The theory of FWI is well-established. However its practical application to 3D seismic datasets is still a subject of intense research. This technique has shown spectacular results in quantitatively extracting P-wave velocities in the shallow near surface at depths of less than 1 km, using wide-angle OBC datasets. This study deals with establishing a robust methodology for the application of FWI that can be routinely applied to analogous field datasets, both in the shallow near surface and at deeper reservoir depths. A practical strategy for anisotropic 3D acoustic FWI was developed and implemented. The stratergy is tested on a series of 3D datasets: (1) a synthetic Marmousi dataset, (2) an OBC field data and (3) a streamer data. A 3D synthetic Marmousi data is used to compare FWI implementations in both the time domain and the frequency domain. In both domains, it was possible to recover an almost ‘perfect’ model with complete data coverage, no noise, and few iterations. Both approaches were useful and competitive, and ideally both should be available within a comprehensive suite of inversion tools. The anisotropic time-domain FWI strategy was successfully implemented to complex OBC field data set with long offsets, full-azimuthal coverage and low frequencies. The FWI quantitatively recovered p-wave velocities in the shallow near surface, at intermediate depths where the sediments are gas bearing, and at deeper reservoir depths. The velocities are indeed realistic and are consistent with an independent reflection PSDM volume, well data and pressure data. The synthetic FWI data better match the field data, with the phase residuals between the two datasets significantly reduced to low values. The gathers are flatter and the depth-migrated images are more resolved and focused. The strategy was also successfully implemented to complex streamer field data set with short offsets, narrow-azimuthal coverage and reduced signal at the low frequencies. The FWI quantitatively recovered P-wave velocities down to depths of 750 m. A complex series of high and low velocity channels are recovered. These are consistent with an independent reflection PSTM volume. The synthetic FWI data better match the field data, with the phase residuals between the two datasets significantly reduced to low values. The depth-migrated images are more resolved and focused in the shallow section. Open Acces